Nonlinear theory of a self-reversing ring stimulated Brillouin scattering mirror

A one-dimensional steady-state theory of stimulated Brillouin scattering in an optical ring resonator is developed allowing for the difference between the phase shifts of the pump and scattered waves in a distance equal to the ring perimeter (channel nonreciprocity). The dependences of the reflection coefficient on the pump intensity are found. It is shown that in the case of a short perimeter the structure of the scattered modes and maximum attainable reflection coefficient are determined by the channel nonreciprocity. It is shown that unidirectional operation is possible in a certain range of parameters. In the case of a long perimeter the frequency-conversion coefficient depends weakly on the difference between the phase shifts of the waves, but multifrequency operation is then possible.